List of top Mathematics Questions on Calculus asked in AP ECET Agricultural Engg, AP ECET Chemical Engg

If $z = x^{2}y^{3} + e^{y}\sin x$, then $\frac{\partial^{2}z}{\partial x\partial y} =$

If $y(x) = x^{x}, x > 0$ then $y''(2) - 2y'(2) =$

If $y + \sin^{-1}(1 - x^{2}) = e^{x}$, then $\frac{dy}{dx} =$

If $2^{x} + 2^{y} = 2^{x+y}$ then $\frac{dy}{dx} =$

If $f(x) = \begin{cases} 4(5^{x}) & x < 0 \\ 8k + x & x \ge 0 \end{cases}$ then $f'(-1) =$

Slope of the tangent to the curve $y = 9x^{2} + 7x^{4} + 5$ at the point $x = 1$ is

If $y = \sqrt{x + \sqrt{x + \sqrt{x + ... \infty}$ then $\frac{dy}{dx} = $

If $y = \frac{(a \cos x + b \sin x + c)}{\sin x}$ then $\frac{dy}{dx} = $

The value of $\lim_{x\rightarrow 0}\frac{\sqrt{1+x} - 1}{x} = $

The value of $\lim_{x\rightarrow\infty}(1 + \frac{1}{x})^{x} = $

If \(u=e^{xy}\), then the value of \[ \frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2} \] at \((1,1)\) is

If \(z=x^2-y^2\), then \[ \frac{1}{x}\frac{\partial z}{\partial x}+ \frac{1}{y}\frac{\partial z}{\partial y} = \]

For what value of \(x\), the function \[ 2x^3+3x^2-36x+10 \] has minimum?

The equation of the tangent to the curve \(y=x^3\) at \((1,1)\) is

Slope of the normal to the curve \[ x^{2/3}+y^{2/3}=2 \] at the point \((1,1)\) is

If \[ y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots}}}, \] then \(\frac{dy}{dx}=\)

\[ \frac{d}{dx}\left(\tan^{-1}\frac{x}{a}\right)= \]

The derivative of \(x^x\) with respect to \(x\) is

The value of \[ \lim_{x\to 1}\left(\frac{x^3-1}{x-1}\right) \] is

The value of \[ \lim_{x\to\infty}\frac{4x^3-x+1}{x^2-4x(1-x^2)} \] is